随机线性拓扑空间

本文首次引入随机线性拓扑空间,并借助于随机线性泛函理论推广了Mackey定理与K.Fan不动点定理.1 随机线性拓扑空间的基本定义及性质定义1 称(E,{xd}dε△为数域K上以概率空间（Ω,σ,μ）为基的随机赋范空间（（△,<）为某一定向集）,如果E是数域上K的线性空间,对任给d∈△,映象xd:E→L+（Ω）（见文[1]）满足下面各条（1）xpd∈L+（Ω）,且如果?d∈△,xpd（ω）=0a,s当且仅当p=θ; （2）xαdp（ω）=（α）xpd（ω）a.s?α∈E,p∈E,d∈△; （3）?e∈△,?d∈△使得?p,q∈E,都有Xp+qe（ω）≤Xpd（ω）+Xqd（ω）a.s;

THE CONDENSATION EXTENSION AND THEMULTIPLE POSITIVE FIXED POINTSOF THE CONDENSING MAPPING

In the paper the authors present some formulae to the condensation extension and k-set contractive extension of a condensing mapping and a k-set contractive mapping respectively, and obtain the sufficient conditions for a condensing mapping to have two or three fixed points. At last they apply their results to solve the generalized H-equation and two-points boundary value problems.